   Chapter 10.5, Problem 25E

Chapter
Section
Textbook Problem

# Identify the type of conic section whose equation is given and find the vertices and foci.25. 4x2 = y2 + 4

To determine

To Find: The type of conic section, vertices and foci for the equation 4x2=y2+4 .

Explanation

Given:

The equation is as follows.

4x2=y2+4 (1).

Rewrite the equation (1) as below.

4x2y2=4

Divide the equation (1) with the value 4 .

4x24y24=44

x21y24=1 (2).

Then, compare the equation (2) with the standard equation of hyperbola.

x2a2y2b2=1

Therefore, the type of conic section is hyperbola.

Calculation:

Compute the center of the hyperbola using the equation:

(xh)2a2+(yk)2b2=1(x0)21(y0)24=1

Therefore, the center of the hyperbola (h,k) is (0,0) .

Substitute the value 1 for a2 and 4 for b2 in equation (2).

a2=1a=1

b2=4b=4b=2

Compute the vertices

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

## Additional Math Solutions

#### Find more solutions based on key concepts 